# ``Order and Optimization (TAC: Vol. III)'' - Typos

This page lists the typographical errors that have been discovered in
the Fall 2006 pre-publication version of
*Order and Optimization*, by Douglas B. West (Volume III of
*The Art of Combinatorics*).
This page is of interest only to the few persons having a copy of this
draft, such as the students in my course and possibly reviewers.
Please send any additional contributions to *west@math.uiuc.edu*.
Contributors noted in parentheses.
## Category 1: Corrections of a Mathematical Nature

- p9, Example 0.24: "
*a*_{0}" should be
"*a*_{1}" (Alexandra Seceleanu)
- p32, Exercise 11.1.5: "
*C*_{i}\times C_{j}" should be
"*\underlin{i}\times \underlin{j}*" (Tim LeSaulnier)
- p41, Example 11.2.20: "the
*k*-shadow of *A* lies in"
should be "the set *A*^{*} of elements covering elements of
*A* is precisely"
- p52, Example 11.3.4: "element of
*BNn*" should be
"member of **2**^{n}:
- p62, Theorem 11.3.18: The chain labeled
*D*_{0} in the
figure should be labeled *D*_{1}. In the text,
"*a*_{3}=3" should be "*a*_{3}=n-1"
- p174, Exercise 12.3.3: "
*2k*-dimensional posets" should be
"posets of dimension at most *2k*".
- p188, Exercise 12.4.2b: in the hint, "at most" should be "at least"
(Paul Wenger)
- p221, top: in the case of one vector having 10 and the other having
01, the intersection remains unchanged if the second vector doesn't change,
so this case should also allow equality.
- p231, Theorem 13.1.31: In the middle paragraph, we must prove that
*B\esub T* in order to put *B* into *H*. This uses the
maximality of *T*. The final paragraph does *not* need the
maximality of *T*.
- p258, Theorem 13.3.3: several instances of "
*I(x)*" and "*C(x)*"
should be "*I(x*_{1})" and "*C(x*_{1})"
- p259, Theorem 13.3.3: At the end of the proof, the claim that
*x*_{i} < I(x_{i-1}) does not follow, but the choice of
*x*_{i} does imply that every element strictly below
*x*_{i} (such as all of *I(x*_{i+1})) is below
all of *I(x*_{i-1}), and this is enough
- p262, Example 13.3.9: "intervals of size
*n*" should be
"intervals of size *i*"
- p479, Theorem 15.3.36: in the last paragraph,
*C'* should be *Y*

## Category 2: Other Changes, Comments and Corrections of Note

- p219, Theorem 13.1.8: the term "shade" was used before its definition
- p223-225, Kruskal-Katona: Uses of "reverse lexicographic" should be
changed to "colex", since some readers might misinterpret "reverse
lexicographic" to mean the reverse of lexicographic order" (Garth Isaak)

## Category 3: Minor Changes, Typos, and Clarifications

- p40, Theorem 11.2.17: "be real-valued weight" should be "be a real-valued
weight"
- p135, Remark 12.2.9: "not surprised" should be "not surprising"
- p228, Theorem 13.1.27: "It suffice" should be "It suffices
- p259, top: "monchromatic" should be "monochromatic", and three lines
later a parenthesis is missing
- p394, Definition 15.1.4: the last "that" should be deleted